Abstract
This paper examines a path-dependent contingent claim called the window double barrier option, including standard but also more exotic features such as combinations of single and double barriers. Price properties and hedging issues are discussed, as well as financial applications.Explicit formulae are provided, along with simple techniques for theirimplementation. Numerical results show that they compare very favourablywith alternative pricing approaches in terms of accuracy and efficiency.
Similar content being viewed by others
References
Bhagavatula, R. S. and P. Carr. (1995). “Valuing Double Barrier Options withTime-Dependent Parameters,” Working Paper, http://www.math.columbia.edu/~pcarr/.
Boyle, P.P. and S.H. Lau. (1994). “Bumping Up Against the Barrier with the Binomial Method,” Journal of Derivatives 1, 6¶14.
Carr, P. (1995). “Two Extensions to Barrier Option Valuation,” Applied Mathematical Finance, 173¶209.
Carr, P., K. Ellis, and V. Gupta. (1998). “Static Hedging of Exotic Options,” Journal of Finance 53, 1165¶1190.
Cox, D.R. and H.D. Miller. (1965). The Theory of Stochastic Processes. Methuen, London.
Cox, J.C., S.A. Ross, and M. Rubinstein. (1979). “Option Pricing: A Simplified Approach,” Journal of Financial Economics 7, 229¶263.
Drezner, Z. and G. O. Wesolowsky. (1989). “On the Computation of the Bivariate Normal Integral,” Journal of Statistics and Computer Simulation 35, 101¶107.
Eydeland, A. and H. Geman. (1995). “Domino Effect: Inverting the Laplace Transform,” RISK, April, 65¶67.
Geman, H. and M. Yor. (1996). “Pricing and Hedging Double-Barrier Options: A Probabilistic Approach,” Mathematical Finance 6 (4), 365¶378.
Genz, A. (2001). “Numerical Computation of Bivariate and Trivariate Normal Probabilities,” preprint, http://ww.sci.wsu.edu/math/faculty/genz/homepage.
Harrison, J.M. and S. Pliska. (1981). “Martingales and Stochastic Integrals in the Theory of Continuous Trading,” Stochastic Processes and their Applications 11, 312¶316.
Heynen, R.C. and H. Kat. (1995). “Partial Barrier Options,” Journal of Financial Engineering 3, 253¶274.
Hui, C.H. (1997). “Time-Dependent Barrier Option Values,” The Journal of Futures Markets 17, 6, 667¶688.
Jarrow, R. and A. Rudd. (1983). Option Pricing. Homewood, IL: Dow Jones-Irwin.
Kunitomo, N. and M. Ikeda. (1992). “Pricing Options with Curved Boundaries,” Mathematical Finance 2 (4), 275¶298.
Luo, L. S. J. (2001). “Various Types of Double-Barrier Options,” Journal of Computational Finance 4 (3), 125¶137.
Niederreiter, H. (1992). Random Number Generation and Quasi Monte Carlo Methods. Philadelphia, PA: SIAM.
Owen, D. B. (1956). “Tables for Computing Bivariate Normal Probability,” Annals of Mathematical Statistics 27, 1075¶1090.
Pelsser, A. (2000). “Pricing Double Barrier Options Using Laplace Transforms,” Finance and Stochastics 4, 95¶104.
Press, W., W. Teukolsky, W. Wetterling, and B. Flannery. (1992). Numerical Recipes in C: The Art of Scientific Computing. Cambridge: CambridgeUniversity Press.
Schmock, U., S. Shreve, and U. Wystup. (1999). “Valuation of Exotic Options Under Short-Selling Constraints,” Working Paper, Carnegie Mellon University.
Sobol, I. M. (1967). “On the Distribution of Points in a Cube and the Approximate Evaluation of Integrals,” USSR Computational Mathematics and Mathematical Physics 7, 86¶112.
Schröder, M. (2000). “On the Valuation of Double-Barrier Options: Computational aspects,” Journal of Computational Finance 3 (4), 5¶33.
Sidenius, J. (1998). “Double Barrier Options: Valuation by Path Counting,” Journal of Computational Finance 1 (3), 63¶79.
Taleb, N. (1997). Dynamic Hedging. NewYork, NY: J. Wiley & Sons.
Toft, K. and C. Xuan. (1998). “How Well Can Barrier Options be Hedged by a Static Portfolio of Standard Options?,” Journal of Financial Engineering 7, 147¶175.
Tong, Y.L. (1990). The Multivariate Normal Distribution. New York, NY: Springer-Verlag.
Trigeorgis, L. (1991). “A Log-Transformed Binomial Numerical Analysis Method for Valuing Complex Multi-Option Investments,” Journal of Financial and Quantitative Analysis 26 (3), 309¶326.
Wystup, U. (1999). “Dealing with Dangerous Digitals,” Working Paper, http://www.mathfinance.de.
Zhang, P.G. (1998). Exotic Options. World Scientific.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Guillaume, T. Window Double Barrier Options. Review of Derivatives Research 6, 47–75 (2003). https://doi.org/10.1023/A:1022874005113
Issue Date:
DOI: https://doi.org/10.1023/A:1022874005113